Alicia is going to sing for the Talent Show. She is very excited and has selected a wonderful song to sing. She has been practicing with her singing teacher for weeks and is feeling very confident about her ability to do a wonderful job.

Her performance outfit is another matter. Alicia has selected a few different skirts and a few different shirts and shoes to wear. Here are her options for shirts

Striped shirt

Solid shirt

Here are her options for skirts.

Blue skirt

Red skirt

Brown skirt

Here are her options for shoes

Dance shoes

Black dress shoes

How many different outfits can Alicia create given these options?

This is best done using a tree diagram. Alicia needs to organize her clothing options using a tree diagram. This Concept will show you all about tree diagrams. When finished, you will know how many possible outfits Alicia can create.

Guidance

Nadia’s soccer team has 2 games to play this weekend. How many outcomes are there for Nadia’s team?

A good way to find the total number of outcomes for events is to make a tree diagram.Atree diagramis a branching diagram that shows all possible outcomes for an event.

To make a tree diagram, split the different events into either-or choices. You can list the choices in any order. Here is a tree diagram for game 1 and game 2.

Step 2: Start the tree diagram by listing any of the choices for Choice 1. Then have Choice 1 branch off to Choice 2. Make sure Choice 2 repeats for each branch of Choice 1.

Step 3: Fill in the third choice. We have left some of the spaces for you to fill in. Double click to check your answers.

Step 4: Fill in the outcomes. Again some of the spaces are left for you to fill in. Double click to check your answers.

You can see that there are 12 possible outcomes for the kitchen design.

Calculate the number of possible outcomes in each example. You can draw a tree diagram to help you.

Example A

Jeff has five different pairs of socks and three pairs of shoes. How many possible combinations are there?

Solution: \begin{align*}15\end{align*} combinations

Example B

Jessie has three sweaters, two turtlenecks and three jackets. How many possible combinations are there?

Solution: \begin{align*}18\end{align*} combinations

Example C

Kelly has chocolate or vanilla ice cream, three choices of toppings and four sauces.

Solution: \begin{align*}24\end{align*} combinations

Here is the original problem once again. Reread it and then look at the tree diagram created.

Alicia is going to sing for the Talent Show. She is very excited and has selected a wonderful song to sing. She has been practicing with her singing teacher for weeks and is feeling very confident about her ability to do a wonderful job.

Her performance outfit is another matter. Alicia has selected a few different skirts and a few different shirts and shoes to wear. Here are her options for shirts

Striped shirt

Solid shirt

Here are her options for skirts.

Blue skirt

Red skirt

Brown skirt

Here are her options for shoes

Dance shoes

Black dress shoes

How many different outfits can Alicia create given these options?

This is best done using a tree diagram. Alicia needs to organize her clothing options using a tree diagram. To do this, we can take each option and create a diagram to show all of the options.

Based on this tree diagram, you can see that Alicia has twelve possible outfits to choose from.

Vocabulary

Tree Diagram

a visual way of showing all of the possible outcomes of an experiment. Called a tree diagram because each option is drawn as a branch of a tree.

Guided Practice

Here is one for you to try on your own.

A local pizza place offers a pizza with several options. On a basic pizza, you can choose one of each option. The options are a sourdough or whole wheat crust, two types of cheese and eight toppings.

Based on these possibilities, how many possible outcomes are there?

Answer

To figure this out, you can draw a tree diagram or you can simply multiply.

Drawing a tree diagram might look nice, but it can take a lot of time.